Massachusetts Comprehensive Assessment System
2012, Grade 10 Mathematics
Question 31: OpenResponse 

Reporting Category: Data Analysis, Statistics, and Probability Standard: 10.D.1  Select, create, and interpret an appropriate graphical representation (e.g., scatterplot, table, stemandleaf plots, boxandwhisker plots, circle graph, line graph, and line plot) for a set of data and use appropriate statistics (e.g., mean, median, range, and mode) to communicate information about the data. Use these notions to compare different sets of data. 
The ages, in years, of the 11 reporters who work at a newspaper are listed below. 28, 45, 61, 40, 55, 58, 33, 27, 35, 33, 46 
 In your Student Answer Booklet, make a stemandleaf plot of the reporters’ ages. Be sure to include a title and a key for your plot.
 What is the range of the ages, in years, of the reporters? Show or explain how you got your answer.
 What is the median age, in years, of the reporters? Show or explain how you got your answer.
The newspaper hired a new reporter. When the age of the new reporter was included in the stemandleaf plot, the range increased by 4 years. What is one possible median age that could result from including the new reporter’s age in the stemandleaf plot? Show or explain how you got your answer.

Scoring Guide and Sample Student Work Select a score point in the table below to view the sample student response.
Score  Description 
4 
The student response demonstrates an exemplary understanding of the Data Analysis, Statistics, and Probability concepts involved in creating and interpreting an appropriate graphical representation for a set of data and using appropriate statistics to communicate information about the data. Given a data set, the student constructs a stemandleaf plot, determines the range and median of the data, and explains how the introduction of a new number affects the data. 
4 
3 
The student response demonstrates a good understanding of the Data Analysis, Statistics, and Probability concepts involved in creating and interpreting an appropriate graphical representation for a set of data and using appropriate statistics to communicate information about the data. Although there is significant evidence that the student was able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result the response merits 3 points. 
2 
The student response demonstrates fair understanding of the Data Analysis, Statistics, and Probability concepts involved in creating and interpreting an appropriate graphical representation for a set of data and using appropriate statistics to communicate information about the data. While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points. 
1 
The student response demonstrates only minimal understanding of the Data Analysis, Statistics, and Probability concepts involved in creating and interpreting an appropriate graphical representation for a set of data and using appropriate statistics to communicate information about the data. 
0 
The student response contains insufficient evidence of an understanding of the Data Analysis, Statistics, and Probability concepts involved in creating and interpreting an appropriate graphical representation for a set of data and using appropriate statistics to communicate information about the data to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Patterns, Relations, and Algebra
 Question 20: Data Analysis, Statistics, and Probability
 Question 21: Number Sense and Operations
 Question 31: Data Analysis, Statistics, and Probability
 Question 41: Patterns, Relations, and Algebra
 Question 42: Measurement
Return to the MCAS 2012 Student Work Directory
Last Updated: June 30, 2016
